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How does multiplying fractions differ from adding fractions??

How does multiplying fractions differ from adding fractions

Example:

$\frac12 + \frac12 = \frac{1+1}{2} = \frac22 = 1$

$\frac12 \times \frac12 = \frac{1\times1}{2\times2} = \frac14$

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